7-5 Congruent Figures Warm Up Find the measure of the third angle in the triangle, given two angle measures. 1. 58°, 104° 2. 32°, 63° 3. 90°, 38° 4. 42°, 88° 18° 85° 90 52° 50° Course 2

7-5 Congruent Figures Objective Today You will learn to identify congruent figures and to use them to find missing measures. Key Math Term Congruent polygons – Are polygons with the same shape and the same size Course 2

Course 2 7-5 Congruent Figures If all of the corresponding sides and angles of two polygons are congruent, then the polygons are congruent. For triangles in particular, the corresponding angles will always be congruent if the corresponding sides are congruent. This is called the Side-Side-Side Rule. Because of this rule, when determining whether triangles are congruent, you only need to determine whether the sides are congruent.

Example 1: Identifying Congruent Triangles 7-5 Congruent Figures Example 1: Identifying Congruent Triangles Determine whether the triangles are congruent. C Q 4 cm 4 cm AB = 4 cm BC = 4 cm AC = 6 cm PQ = 4 cm PR = 4 cm RQ = 5 cm B P 6 cm 5 cm 4 cm 4 cm R A The triangles are not congruent. Although two sides in one triangle are congruent to two sides in the other, the third sides are not congruent. Course 2

7-5 Congruent Figures Try This: Example 2 Determine whether the triangles are congruent. AC = 8 m AB = 6 m BC = 10 m DF = 8 m DE = 6 m EF = 10 m B E 10 m 10 m 6 m 6 m A C F D 8 m 8 m By the Side-Side-Side Rule, ABC is congruent to DEF, or ABC  DEF. If you flip one triangle, it will fit exactly over the other. The notation ABC is read “triangle ABC.” Reading Math Course 2

7-5 Congruent Figures For polygons with more than three sides, it is not enough to compare the measures of their sides. For example, the corresponding sides of the figures below are congruent, but the figures are not congruent. 120 m 70 m 120 m 70 m 145° 35° 35° 145° If you know that two figures are congruent, you can find the missing measures in the figures. Course 2

Additional Example 3A: Using Congruence to Find Missing Measures 7-5 Congruent Figures Additional Example 3A: Using Congruence to Find Missing Measures Determine the missing measures in the set of congruent polygons. The corresponding sides are congruent. The missing side measure is 28 mm. Course 2

Additional Example 3B: Using Congruence to Find Missing Measures 7-5 Congruent Figures Additional Example 3B: Using Congruence to Find Missing Measures Determine the missing measure in the set of congruent polygons. The corresponding angles are congruent. The missing angle measure is 88°. Course 2

Insert Lesson Title Here Course 2 7-5 Congruent Figures Insert Lesson Title Here Try This: Example 3A Determine the missing measure in the set of congruent polygons. 135° The corresponding sides are congruent. 5 ft 120° 6 ft 45° 60° 8 ft The missing side measure is 4 ft. 8 ft 60° 45° 6 ft 5 ft 135° 120° 4 ft

Insert Lesson Title Here 7-5 Congruent Figures Insert Lesson Title Here Try This: Example 3B Determine the missing measure in the set of congruent polygons. 6 ft 5 ft 130° 110° 8 ft The corresponding angles are congruent. 120° 80° 4 ft 100° 10 ft The missing angle measure is 130°. 10 ft 100° 4 ft 80° 120° 8 ft 110° ? 5 ft 6 ft Course 2

Insert Lesson Title Here 7-5 Congruent Figures Insert Lesson Title Here Lesson Quiz 1. Are the triangles congruent? no F D E 5 cm 8 cm A B C 7 cm 5 cm 8 cm 2. Determine the missing measures for the set of congruent polygons. 11 70° 70° 110° c 6 6 6 b 70° 110° 70° 110° 18 a a =11, b =6, c = 110° Course 2